More puzzles done

exercism/fsharp/armstrong-numbers/ArmstrongNumbers.fs

+module ArmstrongNumbers
+
+let intFromChar a = int a - int '0'
+
+// a ^ b where they are both ints
+let rec intPow (a: int) (b: int) =
+    if b = 0 then 1 else a * (intPow a (b - 1))
+
+let isArmstrongNumber (number: int): bool =
+    let len = String.length (string (number))
+    number =
+        (Seq.toList (string (number))
+         |> Seq.fold (fun a c -> a + (intPow (intFromChar c) len)) 0)

exercism/fsharp/armstrong-numbers/ArmstrongNumbers.fsproj

+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <TargetFramework>netcoreapp3.0</TargetFramework>
+
+    <IsPackable>false</IsPackable>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <Compile Include="ArmstrongNumbers.fs" />
+    <Compile Include="ArmstrongNumbersTests.fs" />
+  </ItemGroup>
+
+  <ItemGroup>
+    <PackageReference Include="Microsoft.NET.Test.Sdk" Version="16.6.1" />
+    <PackageReference Include="xunit" Version="2.4.1" />
+    <PackageReference Include="xunit.runner.visualstudio" Version="2.4.1" />
+    <PackageReference Include="FsUnit.xUnit" Version="3.8.1" />
+  </ItemGroup>
+
+</Project>

exercism/fsharp/armstrong-numbers/ArmstrongNumbersTests.fs

+// This file was auto-generated based on version 1.1.0 of the canonical data.
+
+module ArmstrongNumbersTests
+
+open FsUnit.Xunit
+open Xunit
+
+open ArmstrongNumbers
+
+[<Fact>]
+let ``Zero is an Armstrong number`` () =
+    isArmstrongNumber 0 |> should equal true
+
+[<Fact>]
+let ``Single digit numbers are Armstrong numbers`` () =
+    isArmstrongNumber 5 |> should equal true
+
+[<Fact>]
+let ``There are no 2 digit Armstrong numbers`` () =
+    isArmstrongNumber 10 |> should equal false
+
+[<Fact>]
+let ``Three digit number that is an Armstrong number`` () =
+    isArmstrongNumber 153 |> should equal true
+
+[<Fact>]
+let ``Three digit number that is not an Armstrong number`` () =
+    isArmstrongNumber 100 |> should equal false
+
+[<Fact>]
+let ``Four digit number that is an Armstrong number`` () =
+    isArmstrongNumber 9474 |> should equal true
+
+[<Fact>]
+let ``Four digit number that is not an Armstrong number`` () =
+    isArmstrongNumber 9475 |> should equal false
+
+[<Fact>]
+let ``Seven digit number that is an Armstrong number`` () =
+    isArmstrongNumber 9926315 |> should equal true
+
+[<Fact>]
+let ``Seven digit number that is not an Armstrong number`` () =
+    isArmstrongNumber 9926314 |> should equal false
+

exercism/fsharp/armstrong-numbers/README.md

+# Armstrong Numbers
+
+An [Armstrong number](https://en.wikipedia.org/wiki/Narcissistic_number) is a number that is the sum of its own digits each raised to the power of the number of digits.
+
+For example:
+
+- 9 is an Armstrong number, because `9 = 9^1 = 9`
+- 10 is *not* an Armstrong number, because `10 != 1^2 + 0^2 = 1`
+- 153 is an Armstrong number, because: `153 = 1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153`
+- 154 is *not* an Armstrong number, because: `154 != 1^3 + 5^3 + 4^3 = 1 + 125 + 64 = 190`
+
+Write some code to determine whether a number is an Armstrong number.
+
+## Running the tests
+
+To run the tests, run the command `dotnet test` from within the exercise directory.
+
+## Autoformatting the code
+
+F# source code can be formatted with the [Fantomas](https://github.com/fsprojects/fantomas) tool.
+
+After installing it with `dotnet tool restore`, run `dotnet fantomas .` to format code within the current directory.
+
+## Further information
+
+For more detailed information about the F# track, including how to get help if
+you're having trouble, please visit the exercism.io [F# language page](http://exercism.io/languages/fsharp/resources).
+
+## Source
+
+Wikipedia [https://en.wikipedia.org/wiki/Narcissistic_number](https://en.wikipedia.org/wiki/Narcissistic_number)
+

exercism/fsharp/sum-of-multiples/README.md

+# Sum Of Multiples
+
+Given a number, find the sum of all the unique multiples of particular numbers up to
+but not including that number.
+
+If we list all the natural numbers below 20 that are multiples of 3 or 5,
+we get 3, 5, 6, 9, 10, 12, 15, and 18.
+
+The sum of these multiples is 78.
+
+## Running the tests
+
+To run the tests, run the command `dotnet test` from within the exercise directory.
+
+## Autoformatting the code
+
+F# source code can be formatted with the [Fantomas](https://github.com/fsprojects/fantomas) tool.
+
+After installing it with `dotnet tool restore`, run `dotnet fantomas .` to format code within the current directory.
+
+## Further information
+
+For more detailed information about the F# track, including how to get help if
+you're having trouble, please visit the exercism.io [F# language page](http://exercism.io/languages/fsharp/resources).
+
+## Source
+
+A variation on Problem 1 at Project Euler [http://projecteuler.net/problem=1](http://projecteuler.net/problem=1)
+

exercism/fsharp/sum-of-multiples/SumOfMultiples.fs

+module SumOfMultiples
+
+let isMultiple factors number = 
+    List.fold (fun a x -> (a || number % x = 0)) false factors
+
+let sum (factors: int list) (upperBound: int): int = 
+    let goodFactors = List.filter (fun i -> i <> 0) factors
+    let numbers = [ for i in 1..(upperBound - 1) -> i]
+    List.sum (List.filter (fun el -> isMultiple goodFactors el) numbers)

exercism/fsharp/sum-of-multiples/SumOfMultiples.fsproj

+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <TargetFramework>netcoreapp3.0</TargetFramework>
+
+    <IsPackable>false</IsPackable>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <Compile Include="SumOfMultiples.fs" />
+    <Compile Include="SumOfMultiplesTests.fs" />
+  </ItemGroup>
+
+  <ItemGroup>
+    <PackageReference Include="Microsoft.NET.Test.Sdk" Version="16.6.1" />
+    <PackageReference Include="xunit" Version="2.4.1" />
+    <PackageReference Include="xunit.runner.visualstudio" Version="2.4.2" />
+    <PackageReference Include="FsUnit.xUnit" Version="3.8.1" />
+  </ItemGroup>
+
+</Project>

exercism/fsharp/sum-of-multiples/SumOfMultiplesTests.fs

+// This file was auto-generated based on version 1.5.0 of the canonical data.
+
+module SumOfMultiplesTests
+
+open FsUnit.Xunit
+open Xunit
+
+open SumOfMultiples
+
+[<Fact>]
+let ``No multiples within limit`` () =
+    sum [3; 5] 1 |> should equal 0
+
+[<Fact>]
+let ``One factor has multiples within limit`` () =
+    sum [3; 5] 4 |> should equal 3
+
+[<Fact>]
+let ``More than one multiple within limit`` () =
+    sum [3] 7 |> should equal 9
+
+[<Fact>]
+let ``More than one factor with multiples within limit`` () =
+    sum [3; 5] 10 |> should equal 23
+
+[<Fact>]
+let ``Each multiple is only counted once`` () =
+    sum [3; 5] 100 |> should equal 2318
+
+[<Fact>]
+let ``A much larger limit`` () =
+    sum [3; 5] 1000 |> should equal 233168
+
+[<Fact>]
+let ``Three factors`` () =
+    sum [7; 13; 17] 20 |> should equal 51
+
+[<Fact>]
+let ``Factors not relatively prime`` () =
+    sum [4; 6] 15 |> should equal 30
+
+[<Fact>]
+let ``Some pairs of factors relatively prime and some not`` () =
+    sum [5; 6; 8] 150 |> should equal 4419
+
+[<Fact>]
+let ``One factor is a multiple of another`` () =
+    sum [5; 25] 51 |> should equal 275
+
+[<Fact>]
+let ``Much larger factors`` () =
+    sum [43; 47] 10000 |> should equal 2203160
+
+[<Fact>]
+let ``All numbers are multiples of 1`` () =
+    sum [1] 100 |> should equal 4950
+
+[<Fact>]
+let ``No factors means an empty sum`` () =
+    sum [] 10000 |> should equal 0
+
+[<Fact>]
+let ``The only multiple of 0 is 0`` () =
+    sum [0] 1 |> should equal 0
+
+[<Fact>]
+let ``The factor 0 does not affect the sum of multiples of other factors`` () =
+    sum [3; 0] 4 |> should equal 3
+
+[<Fact>]
+let ``Solutions using include-exclude must extend to cardinality greater than 3`` () =
+    sum [2; 3; 5; 7; 11] 10000 |> should equal 39614537
+